Math 2414 Calculus II Information
LSC-CyFair Math Department
Catalog Description
Differentiation and integration of exponential and logarithmic functions, techniques of integration, applications of the definite integral, the calculus of transcendental functions, parametric equations, polar coordinates, indeterminate forms, improper integrals, L’Hopital’s Rule, sequences and series.
The student will:
• Use the concepts of definite integrals to solve problems involving area, volume, work, and other physical applications.
• Use substitution, integration by parts, trigonometric substitution, partial fractions, and tables of anti-derivatives to evaluate definite and indefinite integrals.
• Define an improper integral.
• Apply the concepts of limits, convergence, and divergence to evaluate some classes of improper integrals.
• Determine convergence or divergence of sequences and series.
• Use Taylor and MacLaurin series to represent functions.
• Use Taylor or MacLaurin series to integrate functions not integrable by conventional methods.
• Use the concept of parametric equations and polar coordinates to find areas, lengths of curves, and representations of conic sections.
• Apply L'hôpital's Rule to evaluate limits of indeterminate forms.
Credit Hours: 4
Lecture Hours: 3
Lab Hours: 2
External Hours: 0
Total Contact Hours: 80
MATH 2413;
ENGL 0305 or ENGL 0365 OR higher level course (ENGL 1301), OR placement by testing
ENGL 0307
Required Materials
Textbook:
Textbook Plus Maple Software and MyMathLab Portal Access: 9781256368731
Textbook Only: 9780321471963
MyMathLab Portal Access Only: 9780558357603
Calculator:
Calculators capable of symbolic manipulation will not be allowed on tests. Examples include, but are not limited to, TI 89, TI 92, and Nspire CAS models and HP 48 models.
Neither cell phones nor PDA’s can be used as calculators. Calculators may be cleared before tests.
Differentiation and Integration Formulas:
Students are expected to memorize the differentiation formulas on the last page inside the back cover of the text and integration formulas 1- 20 in the attached chart.
Textbook Sections
Chapter 7. Transcendental Functions
7.1 Inverse Functions and their Derivatives
7.2 Natural Logarithms
7.3 Exponential Functions
7.4 Inverse Trigonometric Functions
7.5 Exponential Change and Separable Differential Equations
7.6 Indeterminate Forms and L'Hôpital's Rule
7.7 Hyperbolic Functions
Chapter 8. Techniques of Integration
8.1 Integration by Parts
8.2 Trigonometric Integrals
8.3 Trigonometric Substitutions
8.4 Integration of Rational Functions by Partial Fractions
8.5 Integral Tables and Computer Algebra Systems
8.6 Numerical Integration
8.7 Improper Integrals
Chapter 9. Infinite Sequences and Series
9.1 Sequences
9.2 Infinite Series
9.3 The Integral Test
9.4 Comparison Tests
9.5 The Ratio and Root Tests
9.6 Alternating Series, Absolute and Conditional Convergence
9.7 Power Series
9.8 Taylor and Maclaurin Series
9.9 Convergence of Taylor Series
Chapter 10. Polar Coordinates and Conics
10.1 Polar Coordinates
10.2 Graphing in Polar Coordinates
10.3 Areas and Lengths in Polar Coordinates
10.4 Conic Sections (review)
10.5 Conics in Polar Coordinates
